具有2-反射外尔群的Lorentzian Kac-Moody代数
Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections
摘要：
本文描述了一个新的大类Lorentzian Kac-Moody代数。对于所有的秩，我们分类2-反射双曲格S的2-反射的有限体积和一个格Weyl向量的组。它们定义了相应的限制算术型双曲Kac-Moody代数，这些代数是S分次的.对于其中的大多数，我们构造了Lorentzian Kac-Moody代数，给出了它们的自守修正：它们由S分次，具有相同的单实根，但它们的分母恒等式由具有2-反射因子的自守形式给出。我们给出了这些自守形式的精确构造作为Borcherds产品，在某些情况下，作为添加剂Jacobi提升。
英文摘要：
We describe a new large class of Lorentzian Kac--Moody algebras. For all ranks, we classify 2-reflective hyperbolic lattices S with the group of 2-reflections of finite volume and with a lattice Weyl vector. They define the corresponding hyperbolic Kac--Moody algebras of restricted arithmetic type which are graded by S. For most of them, we construct Lorentzian Kac--Moody algebras which give their automorphic corrections: they are graded by the S, have the same simple real roots, but their denominator identities are given by automorphic forms with 2-reflective divisors. We give exact constructions of these automorphic forms as Borcherds products and, in some cases, as additive Jacobi liftings.
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